4.9. HL Triangle Congruence http://www.ck12.org
Example A
What information would you need to prove that these two triangles are congruent using the HL Theorem?
For HL, you need the hypotenuses to be congruent. So,AC∼=MN.
Example B
Determine if the triangles are congruent. If they are, write the congruence statement and which congruence postulate
or theorem you used.
We know the two triangles are right triangles. The have one pair of legs that is congruent and their hypotenuses are
congruent. This means that 4 ABC∼= 4 RQPby HL.
Example C
Determine the additional piece of information needed to show the two triangles are congruent by HL.
We already know one pair of legs is congruent and that they are right triangles. The additional piece of information
we need is that the two hypotenuses are congruent,U T∼=F G.
Watch this video for help with the Examples above.
MEDIA
Click image to the left for more content.CK-12 Foundation: Chapter4HLTriangleCongruenceB
Vocabulary
Two figures arecongruentif they have exactly the same size and shape. By definition, two triangles arecongruent
if the three corresponding angles and sides are congruent. The symbol∼=means congruent. There are shortcuts
for proving that triangles are congruent. TheHL Triangle Congruence Theoremstates that if the hypotenuse and
leg in one right triangle are congruent to the hypotenuse and leg in another right triangle, then the two triangles are
congruent. Aright trianglehas exactly one right (90◦) angle. The two sides adjacent to the right angle are called
legsand the side opposite the right angle is called thehypotenuse. HL can only be used with right triangles.
Guided Practice
- Determine if the triangles are congruent. If they are, write the congruence statement and which congruence
postulate or theorem you used. - Fill in the blanks in the proof below.
Given:
SV⊥WU
Tis the midpoint ofSVandWU
Prove:W S∼=UV